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BXMY is cyclic

Source: All Russian 2014 Grade 10 Day 2 P2

May 3, 2014

geometrypower of a pointgeometry proposed

Problem Statement

Let

M

be the midpoint of the side

AC

of

\triangle ABC

. Let

P\in AM

and

Q\in CM

be such that

PQ=\frac{AC}{2}

. Let

(ABQ)

intersect with

BC

at

X\not= B

and

(BCP)

intersect with

BA

at

Y\not= B

. Prove that the quadrilateral

BXMY

is cyclic.
F. Ivlev, F. Nilov

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